Summary
In this paper, a combination model based on the Mises yield criterion which considers simultaneously the expansion (or the contraction) and the translation of the yield surface is treated. The stress-strain relations of this model are applied to the numerical analysis of the elastic-plastic circular plates.
Übersicht
Es wird ein kombiniertes Fließmodell vorgeschlagen, das auf der v. Mises'schen Fließbedingung aufbaut, aber gleichzeitig die Dehnung (oder die Kontraktion) und die Verschiebung der Fließfläche berücksichtigt. Die Spannungs-Dehmmgs-Beziehungen dieses Modells werden auf die numerische Berechnung von elastischplastischen Kreisplatten angewendet.
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References
Marcal, P. V.: A Stiffness Method for Elastic-Plastic Problems. Int. J. Mech. Sci. 7 (1965) p. 229.
Marcal, P. V.; King, I. P.: Elastic-Plastic Analysis of Two-Dimensional Stress Systems by the Finite Element Method. Int. J. Mech. Sci. 9 (1967) p. 143.
Yamada, Y.; Yoshimura, N.; Sakurai, T.: Plastic Stress-Strain Matrix and Its Application for the Solution of Elastic-Plastic Problems by the Finite Element Method. Int. Mech. J, Sci. 10 (1968) p. 343.
Hamada, M.; Tanaka, M.: A Numerical Method for Solving Elastic-Plastic Problems of Rotationally Symmetric Shells. Trans. Japan Soc. Mech. Engrs. (in Japanese) 36–292 (1970) p. 1977; Bulletin of the JSME 14–74 (1971), P. 724.
Hamada, M.; Tanaka, M.: A Numerical Method Considering the Bauschinger Effect for Large Deflection Analysis of Elastic-Plastic Circular Plates. Trans. Japan Soc. Mech. Engrs. (in Japanese) 38–305 (1972), p. 36 (to be published on Bulletin of the JSME, 15–87, 1972).
Hill, R.: The Mathematical Theory of Plasticity. Oxford 1950.
Prager, W.: The Theory of Plasticity: A Survey of Recent Achievements. Proc. Inst. Mech. Engrs. 169 (1955) P. 41.
Prager, W.: A New Method of Analyzing Stresses and Strains in Work-Hardening Plastic Solids. J. Appl. Mech. 23 (1956) p. 493.
Shield, R. T.; Ziegler, H.: On Prager's Hardening Rule. Z. Angew. Math. Phys. 9a (1958) S. 260.
Ziegler, H.: A Modification of Prager's Hardening Rule. Quart. Appl. Math. 17 (1959) p. 55.
Hodge, P. G., Jr.: Discussion of [8]. J. Appl. Mech. 24 (1957) P. 482.
Perrone, N.; Hodge, P. G., Jr.: Strain Hardening Solutions with Generalized Kinematic Models. Proc. 3rd. U.S.Natl. Congr. Appl. Mech. 1958, p. 641.
Igaki, H.; Sugimoto, M.; Saito, K.: Anisotropic Yield Criterion under the Maximum Shear Stress Theory. Trans. Japan Soc. Mech. Engrs. (in Japanese) 35–279 (1969) p. 2125.
Shiratori, E.; Ikegami, K.: Experimental Study of the Subsequent Yield Surface by Using Cross-Shaped Specimens. J. Mech. Phys. Solids 16 (1968) p. 373.
Szczepiński, W.; Miastkowski, J.: An Experimental Study of the Effect of the Prestraining History on the Yield Surfaces of an Aluminium Alloy. J. Mech. Phys. Solids 16 (1968) p. 153.
Mróz, Z.: On the Description of Anisotropic Workhardening. J. Mech. Phys. Solids 15 (1967) p. 163.
Reissner, E.: Rotationally Symmetric Problems in the Theory of Thin Elastic Shells. Proc. 3rd. U.S. Natl. Congr. Appl. Mech. 1958, p. 51.
Ohashi, Y.; Murakami, S.: Large Deflection in Elastoplastic Bending of a Simply Supported Circular Plate under a Uniform Load. Trans. ASME, Ser. E 33 (1966) p. 866.
Timoshenko, S.; Krieger, S. W.: Theory of Plates and Shells. New York and London 1959, p. 51.
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The author wishes to express his thanks to Prof. Dr. M. Hamada, Dr. K. Saito, Dr. H. Igaki, Prof. Dr. H. Ziegler and Mr. T. Nakatani for their help in performing this work.
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Tanaka, M. Large deflection analysis of elastic-plastic circular plates with combined isotropic and kinematic hardening. Ing. arch 41, 342–356 (1972). https://doi.org/10.1007/BF00533081
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DOI: https://doi.org/10.1007/BF00533081